Question Number 219602 by deleted50 last updated on 29/Apr/25
$$\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{d}{t}\:{e}^{−\boldsymbol{{i}}{kt}} {J}_{−\frac{\mathrm{2}}{\mathrm{3}}} \left({t}\right)−\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{d}{t}\:{e}^{−\boldsymbol{{i}}{kt}} {Y}_{−\frac{\mathrm{2}}{\mathrm{3}}} \left({t}\right)=?? \\ $$
Commented by Nicholas666 last updated on 29/Apr/25
$${nice}\:{problem} \\ $$
Commented by Nicholas666 last updated on 29/Apr/25
https://www.quora.com/profile/Bekicot-5/Solution-math-int_0-infty-dt-e-ikt-J_-2-3-t-int_0-infty-dt-e-ikt-Y_-2-3-t-math-math-m?ch=10&oid=221092585&share=4820445c&srid=5Xg5SU&target_type=post
Answered by Nicholas666 last updated on 29/Apr/25
$$\frac{\left(\sqrt{\mathrm{3}}+\mathrm{1}\right)\left({ik}+\sqrt{\mathrm{1}−{k}^{\mathrm{2}} }\right)^{\mathrm{2}/\mathrm{3}} +\left({ik}+\sqrt{\mathrm{1}−{k}^{\mathrm{2}} }\right)^{−\mathrm{2}/\mathrm{3}} }{\:\sqrt{\mathrm{3}}\sqrt{\mathrm{1}−{k}^{\mathrm{2}} }} \\ $$